CLASSIFICATION OF COXETER GROUPS WITH FINITELY MANY ELEMENTS OF a-VALUE 2
نویسندگان
چکیده
We consider Lusztig’s a-function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of a-value 2 in terms of Coxeter diagrams.
منابع مشابه
On the Maximally Clustered Elements of Coxeter Groups
We continue the study of the maximally clustered elements for simply laced Coxeter groups which were recently introduced by Losonczy. Such elements include as a special case the freely braided elements of Losonczy and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. Our main result is to classify the MC-finite Coxeter groups, namely those Coxeter groups havin...
متن کاملBraided Elements in Coxeter Groups , Ii
We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work. A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that...
متن کاملSimplicity of the Reduced C-algebras of Certain Coxeter Groups
Let (G, S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C∗-algebra of G is simple with unique normalised trace. For an arbitrary finitely generated Coxeter group we prove the validity of a Haagerup inequality: There exist constants C > 0 and Λ ∈ N such that for a f...
متن کاملOn the Fully Commutative Elements of Coxeter Groups
Let W be a Coxeter group. We define an element w ~ W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting generators. We give several combinatorial characterizations of this property, classify the Coxeter groups with finitely many fully commutative elements, and classify the parabolic quotients whose membe...
متن کاملOn the Isomorphism Problem for Finitely Generated Coxeter Groups. I Basic Matching
The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper, we determine some stro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2018